\beamer@endinputifotherversion {3.10pt}
\select@language {english}
\beamer@sectionintoc {1}{Over view}{3}{0}{1}
\beamer@sectionintoc {2}{Introduction}{5}{0}{2}
\beamer@sectionintoc {3}{Preliminaries and notation}{8}{0}{3}
\beamer@subsectionintoc {3}{1}{Basic notation}{8}{0}{3}
\beamer@subsectionintoc {3}{2}{Orientable}{10}{0}{3}
\beamer@sectionintoc {4}{Orientability issues}{17}{0}{4}
\beamer@subsectionintoc {4}{1}{over view of this section}{17}{0}{4}
\beamer@subsectionintoc {4}{2}{Continuous line fields on arbitrary domains}{18}{0}{4}
\beamer@subsectionintoc {4}{3}{Arbitrary line fields on simply-connected domains}{23}{0}{4}
\beamer@sectionintoc {5}{Analytic orientability criteria in 2D}{24}{0}{5}
\beamer@subsectionintoc {5}{1}{Preliminary}{24}{0}{5}
\beamer@subsectionintoc {5}{2}{Important Propostions}{27}{0}{5}
\beamer@subsectionintoc {5}{3}{The final lemmas of this section}{29}{0}{5}
\beamer@sectionintoc {6}{Enegy minimizing}{32}{0}{6}
